A hot wire air flow rate meter in a motor vehicle is known in which the hot wire is burned off to remove dirt particles after each shutoff of the engine. This is accomplished by means of a predefined imbalance of a bridge circuit, in which the hot wire represents one of the bridge resistors. In principle, this continuously recurring burnoff produces good results; however, the service life of the hot wire is shortened thereby. In addition, experience has shown that a frequent burnoff at a relatively low temperature (ca. 850.degree. C.) burns off only organic soil particles, but cannot prevent the deposit of silicate glasses. These silicate glasses are formed from road dust and they impair the measurement result. It has been found that these silicate glasses can be melted off from the hot wire at high temperatures (ca. 1200.degree. C.), but this procedure involves changes in the surface of the wire and in the characteristic curve brought about as a result of thermal etching of the surfaces of the hot wire.